(x-2)(x+1)=10

Solution for (x-2)(x+1)=10 equation:

Simplifying
(x + -2)(x + 1) = 10

Reorder the terms:
(-2 + x)(x + 1) = 10

Reorder the terms:
(-2 + x)(1 + x) = 10

Multiply (-2 + x) * (1 + x)
(-2(1 + x) + x(1 + x)) = 10
((1 * -2 + x * -2) + x(1 + x)) = 10
((-2 + -2x) + x(1 + x)) = 10
(-2 + -2x + (1 * x + x * x)) = 10
(-2 + -2x + (1x + x2)) = 10

Combine like terms: -2x + 1x = -1x
(-2 + -1x + x2) = 10

Solving
-2 + -1x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-2 + -10 + -1x + x2 = 10 + -10

Combine like terms: -2 + -10 = -12
-12 + -1x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-12 + -1x + x2 = 0

Factor a trinomial.
(-3 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-3, 4}